A 4-digit palindrome has form ABBA. Its digit sum is A+B+B+A=2A+2B=2(A+B). For divisibility by 9, 2(A+B) must be divisible by 9, so A+B must be divisible by 9. A ranges 1-9, B ranges 0-9. Possible A+B=9 or 18. For 9: (1,8)(2,7)...(8,1)(9,0) → 9 pairs. For 18: (9,9) → 1 pair. Total 10.